$h(x) = x^{2}$ $f(x) = -7x^{2}+4(h(x))$ $g(t) = -t^{3}-4t^{2}+2(f(t))$ $ g(f(0)) = {?} $
Solution: First, let's solve for the value of the inner function, $f(0)$ . Then we'll know what to plug into the outer function. $f(0) = -7(0^{2})+4(h(0))$ To solve for the value of $f$ , we need to solve for the value of $h(0)$ $h(0) = 0^{2}$ $h(0) = 0$ That means $f(0) = -7(0^{2})+(4)(0)$ $f(0) = 0$ Now we know that $f(0) = 0$ . Let's solve for $g(f(0))$ , which is $g(0)$ $g(0) = -0^{3}-4(0^{2})+2(f(0))$ To solve for the value of $g$ , we need to solve for the value of $f(0)$ $f(0) = -7(0^{2})+4(h(0))$ To solve for the value of $f$ , we need to solve for the value of $h(0)$ $h(0) = 0^{2}$ $h(0) = 0$ That means $f(0) = -7(0^{2})+(4)(0)$ $f(0) = 0$ That means $g(0) = -0^{3}-4(0^{2})+(2)(0)$ $g(0) = 0$